Chapter 11 - Quantum Impedance of Electrons

Abstract

In the electromagnetic case, the wave nature leads to a wave impedance of free space which is purely real. The wave impedance of waveguides is different, depending on the propagation constants. The characteristic impedance of a waveguide contains further geometrical factors. These three are all different, yet share the same origin, the wave nature of photons. The chapter derives the wave impedances for electrons in free space, in a quantum wire, or in electron quantum waveguide (EQW), for both open and closed systems. This chapter identifies the so-called universal conductance as the input conductance from a contact to a structure, whether a section of a Qwire, a quantum well , or a quantum dot . It explores why experimental data give unity for the transmission. At low temperatures, different modes from different transverse degree of freedoms are truly independent. As soon as mixing of the longitudinal and transverse mode is presented, longitudinal and transverse momenta are mixed, and these equal steps of conductance are smeared.